This paper introduces the design of SymGrid, a new Grid framework that will, for the first time, allow multiple invocations of symbolic computing applications to interact via the Grid. SymGrid is designed to support the specific needs of symbolic computation, including computational steering (greater interactivity), complex data structures, and domain-specific computational patterns (for irregular parallelism). A key issue is heterogeneity: SymGrid is designed to orchestrate components from different symbolic systems into a single coherent (possibly parallel) Grid application, building on the OpenMath standard for data exchange between mathematically- oriented applications. The work is being developed as part of a major EU infrastructure project. © Springer-Verlag Berlin Heidelberg 2007.